Yes, absolutely. This video with Adam Savage is a pretty good one for the visuals and walk-around experience, and they talk about the hand-made-ness feeling you get from seeing the orbiter. This is Discovery at the National Air and Space Museum but Endeavour (which I've seen) feels very similar to experience. I have a strong recollection of seeing Endeavour and really being impacted by the gimballing mount of the main engines; I don't know how I thought they worked before, maybe some sort of flexible rubber interface that would flex as the engines moved in order to ensure a seal around the engine, but they are ball joints that rotate in a socket and presumably have some sort of O-ring seal. And that's such a simple, straightforward, mundane solution for how to get the engines freedom of movement that it was a real "of course that's how they did it" feeling. It's a moment of "wait a second, that's the same thing as how my 25 dollar shower head moves around to adjust its aim" feeling. You can see details that you just don't get otherwise, like the wear on the inside of the engine bells from repeatedly spitting out hellfire.

tl;dr: definitely go see it if you can

It's absolutely discernable, moreso in person than in photos. Pretty cool to see such a complex machine just ... covered in what looks like felt.

I’m not sure, but you can walk underneath the shuttle, so the bottom tiles are about 10 feet away!